#Quadratic inequalities how to#

Test and improve your knowledge of Quadratic Inequalities with example questins and answers

Inequalities Practice Questions: Quadratic Inequalities.

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Inequalities Revision Notes: Quadratic Inequalities.

Helps other - Leave a rating for this tutorial (see below) Solving Quadratic Inequalities by Studying the SignĮnjoy the 'Quadratic Inequalities' math tutorial? People who liked the 'Quadratic Inequalities' tutorial found the following resources useful: Inequalities Learning Material Tutorial ID Please select a specific 'Quadratic Inequalities' lesson from the table below, review the video tutorial, print the revision notes or use the practice question to improve your knowledge of this math topic.

Therefore, we are dedicating this entire tutorial only to quadratic inequalities. Obviously, such inequalities are more complicated to solve compared to linear ones. inequalities that contain one of the variables in the second power.

#Quadratic inequalities how to#

Now, we will explain how to solve quadratic inequalities, i.e. In the previous tutorial, we explained how to solve linear inequalities in one or two variables. How to find the solution set(s) of a quadratic inequality?.How to study the sign of a quadratic inequality?.What happens to the sign of a quadratic inequality when the discriminant is positive? Zero? Negative?.How to write a quadratic inequality in the standard form?.How to identify whether a given number is a root of a quadratic inequality or not?.Therefore, -2 < x < 3 is the solution.Inequalities Learning Material Tutorial ID Multiply the entire expression by -1 and change the inequality signīy applying the rule (x – a) (x – b) ≥ 0, then a ≤ x ≤ b, we can comfortably write the solutions of this quadratic inequality as:īecause y is negative for x 2 − x − 6 < 0, then we choose an interval in which the curve will be below the x axis. The curve for x 2 − 3x + 2 > 0 has positive y, therefore which choose the values of x in which the curve will be above the x-axis. Now solve for the roots of the inequality as Therefore, the solution to the quadratic inequality is 1 ≤ x ≤ 2 Multiply the quadratic equation by -1 and remember to change the sign.įor, x – 2 = 0 ⟹ x = 2 and for, x – 1= 0 ⟹x=1 Therefore, x ≤ -3 or x ≥5/2 is the solution. Since the y for 2x 2 + x − 15 ≤ 0 is negative, the we choose the values of x in which the curve will be below the x axis. The values x 4 are therefore the solution of this quadratic inequality.įor, 2x – 5 = 0 ⟹ x= 5/2 and for, x + 3= 0 ⟹ x = -3 To write the inequality in standard form, subtract both sides of the inequality by 12.įactorize the quadratic inequality to get to Since y is positive, we therefore choose the values of x which the curve will be above the x-axis. Solve for all the zeroes for the inequality įor, (x – 1) > 0 ⟹ x > 1 and for, (x – 3) > 0 ⟹ x>3 If the quadratic inequality is in the form: (x – a) (x – b) ≥ 0, then a ≤ x ≤ b, and if it is in the form :(x – a) (x – b) ≤ 0, when a –3įirst, make one side one side of the inequality zero by adding both sides by 3.Write the solution in inequality notation or interval notation.Write the quadratic inequality in standard form: ax 2 + bx + c where a, b and are coefficients and a ≠ 0.

To solve a quadratic inequality, we also apply the same method as illustrated in the procedure below: Therefore, the roots of the quadratic equation are, x = 2, -4/3. Since we know we can similarly solve quadratic inequalities as quadratic equations, it is useful to understand how to factorize the given equation or inequality.įactorize the expression on the left-hand side. How Quadratic Equations are Solved by Factorization Method? Before we can learn how to solve quadratic inequalities, let’s recall how quadratic equations are solved by handling a few examples. Quadratic equations can be solved by either the factorization method or by use of the quadratic formula. The only exception is that, with quadratic equations, you equate the expressions to zero, but with inequalities, you’re interested in knowing what’s on either side of the zero i.e. Solving a quadratic inequality in Algebra is similar to solving a quadratic equation. A quadratic inequality is an equation of second degree that uses an inequality sign instead of an equal sign.Įxamples of quadratic inequalities are: x 2 – 6x – 16 ≤ 0, 2x 2 – 11x + 12 > 0, x 2 + 4 > 0, x 2 – 3x + 2 ≤ 0 etc.